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Figure 4 | EPJ Quantum Technology

Figure 4

From: Fermionic models with superconducting circuits

Figure 4

Probability \(\pmb{Pij}\) for each state \(\pmb{|ij\rangle}\) in the Hubbard model with two fermionic modes. We obtain the same dynamics for hopping \(h=1\), and values of the potential \(U=1\) and \(U=0.5\). We also consider in both cases different number of Trotter steps, \(n=4\) and \(n=10\), and observe the same result with no Trotter error. The initial state is in all cases \((|00\rangle+ |10\rangle)/\sqrt{2}\). Dashed lines refer to numerical solutions without Trotter approximation, and solid lines to numerical solutions with Trotter approximation. The absence of Trotter error comes from the fact that the second term in the Trotter expansion in Eq. (1), i.e., the term proportional to the sum of commutators, is zero for this specific model, allowing us to perform the simulation in a single Trotter step.

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